Equivalence of Forms
Every quadratic form q in n variables over a field of characteristic not equal to 2 is equivalent to a diagonal form
Such a diagonal form is often denoted by .
Classification of all quadratic forms up to equivalence can thus be reduced to the case of diagonal forms.
Read more about this topic: Quadratic Form
Famous quotes containing the word forms:
“A strange effect of marriage, such as the nineteenth century has made it! The boredom of married life inevitably destroys love, when love has preceded marriage. And yet, as a philosopher has observed, it speedily brings about, among people who are rich enough not to have to work, an intense boredom with all quiet forms of enjoyment. And it is only dried up hearts, among women, that it does not predispose to love.”
—Stendhal [Marie Henri Beyle] (1783–1842)